The measurement of the nuclear magnetic properties of a subterranean formation, and in particular, the quantification of certain properties resulting from or indicative of the presence or absence of hydrogen atoms (and hence, the presence or absence of hydrocarbons), is commonly practiced in the art. The basic core and log NMR measurements, and in particular those commonly referred to as T2 decay measurements, may be presented as a distribution of T2 amplitudes versus time at each of one or more sample depths.
It is widely known among practitioners of NMR exploration projects that T2 decay data may be further processed to derive total pore volume values (the total porosity) and pore volumes within different ranges of T2. The most common volumes are bound fluid and free fluid. A permeability estimate can be derived from T2 distribution data using a transform such as the Timur-Coates transform and/or the SDR permeability transform, among many others known to those of ordinary skill in the art. By running the log with different acquisition parameters, direct hydrocarbon typing and enhanced diffusion are possible.
NMR exploration methodologies are based upon the fact that the nuclei of many elements (and in particular, hydrogen) have angular momentum (spin) and a magnetic moment. The nuclei have a characteristic frequency of oscillation, known to those of ordinary skill in the art as the Larmor frequency, which is related to the magnitude of the magnetic field in their locality.
In typical implementations, there are two phases to NMR measurement: polarization and acquisition. First, the nuclear spins of nuclei in the exploration region are brought into alignment (polarized) by means of introducing a static magnetic field (BO), resulting in a net magnetization. The nuclear polarization takes a characteristic time T1 to achieve equilibrium. Second, the equilibrium state is disrupted or “tipped” by a burst from an oscillating magnetic field. The oscillating magnetic field is designed to tip the nuclear spins with resonant frequency within the bandwidth of the oscillating magnetic field away from the static field direction. After tipping, the spins precess around the static field at a particular frequency known as the Larmor frequency.
At the end of a “tipping” pulse, spins on resonance are pointed in a common direction, and they precess at the Larmor frequency. However, due to such factors as inhomogeneity in the static field, imperfect instrumentation, or microscopic material inhomogeneities, each nuclear spin precesses at a slightly different rate than the others. Thus, after time, the spins will no longer be precessing in phase with one another. This “dephasing” as it is known can be accounted for using known techniques, for example, generating spin “echoes” by applying a series of pulses to repeatedly refocus the spin system. The decay (time constant) of echo amplitude correlates in known fashion by properties of the material being explored, and is commonly quantified as a so-called T2 relaxation value.
Furthermore, it has been shown that echo amplitude decay is composed of a plurality of different decay components, forming what is known as a “T2 distribution.”
The foregoing description of polarization and acquisition phases of a NMR study provides a summary of concepts (such as T2 distributions and the Larmor frequency) and processes (such as data transforms) that, while complex and likely beyond the scope of a hypothetical average person's knowledge or familiarity, would be understood and well within the range of expertise of a person of ordinary skill in this particular art.
Those of ordinary skill in the art will be also be aware that the well-known CPMG cycle of radio frequency pulses designed by Carr, Purcell, Meiboom and Gill may be used to produce echo trains appropriate for NMR measurements.
In a standard CPMG sequence, an initial electromagnetic (typically radio frequency) pulse is applied long enough to “tip” the protons into a plane perpendicular to the static magnetic field (the 90° pulse). Initially the protons precess in unison, producing a large signal in the antenna, but then quickly dephase due to the inhomogeneities. Another pulse is applied, long enough to reverse their direction of precession (the 180° pulse), and causing them to come back in phase again after a short time. Being in phase, they produce another strong signal called an echo. They quickly dephase again but can be rephased by another 180° pulse. Rephasing may be (and customarily is) repeated many times, while measuring the magnitude of each echo. The echo magnitude decreases with time due to the molecular relaxation mechanism's surface, bulk, and diffusion, among other factors. One “measurement” typically may comprise many hundreds of echoes in a so-called echo train, where the time between each echo (the echo spacing TE) is of the order of 1 ms or less.
NMR measurements made by both laboratory instruments and logging tools follow the same principles very closely. An important feature of NMR measurement is the time needed to acquire it. In the laboratory, time presents no difficulty. In practice, there is a trade-off between the time needed for polarization and acquisition, logging speed and frequency of sampling. The longer the polarization and acquisition, the more complete the measurement. However, the longer times require either lower logging speed or less frequent samples.
In the prior art, an NMR log analysis has been performed on a deterministic basis, which is based on the fundamental equations governing the NMR relaxation process. Although this is an acceptable approach, there is a perceived drawback in that it requires reliable, a priori knowledge of the NMR properties of the fluids in the formation, to be used as constraints in the inversion algorithms used for calculating T2 relaxation distributions.